Fraction calculator



The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.

Result:

1.5 - 1 1/5 = 3/10 = 0.3

Spelled result in words is three tenths.

How do you solve fractions step by step?

  1. Conversion a decimal number to a fraction: 1.5 = 15/10 = 3/2

    a) Write down the decimal 1.5 divided by 1: 1.5 = 1.5/1
    b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
    1.5/1 = 15/10
    Note: 15/10 is called a decimal fraction.

    c) Simplify and reduce the fraction
    15/10 = 3 * 5/2 * 5 = 3 * 5/2 * 5 = 3/2
  2. Conversion a mixed number 1 1/5 to a improper fraction: 1 1/5 = 1 1/5 = 1 · 5 + 1/5 = 5 + 1/5 = 6/5

    To find new numerator:
    a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5
    b) Add the answer from previous step 5 to the numerator 1. New numerator is 5 + 1 = 6
    c) Write a previous answer (new numerator 6) over the denominator 5.

    One and one fifth is six fifths
  3. Subtract: 1.5 - 6/5 = 3/2 - 6/5 = 3 · 5/2 · 5 - 6 · 2/5 · 2 = 15/10 - 12/10 = 15 - 12/10 = 3/10
    For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 5) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 5 = 10. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - three halfs minus six fifths = three tenths.

Rules for expressions with fractions:

Fractions - use the slash “/” between the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

The colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2


Examples:

adding fractions: 2/4 + 3/4
subtracting fractions: 2/3 - 1/2
multiplying fractions: 7/8 * 3/9
dividing Fractions: 1/2 : 3/4
exponentiation of fraction: 3/5^3
fractional exponents: 16 ^ 1/2
adding fractions and mixed numbers: 8/5 + 6 2/7
dividing integer and fraction: 5 ÷ 1/2
complex fractions: 5/8 : 2 2/3
decimal to fraction: 0.625
Fraction to Decimal: 1/4
Fraction to Percent: 1/8 %
comparing fractions: 1/4 2/3
multiplying a fraction by a whole number: 6 * 3/4
square root of a fraction: sqrt(1/16)
reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
expression with brackets: 1/3 * (1/2 - 3 3/8)
compound fraction: 3/4 of 5/7
fractions multiple: 2/3 of 3/5
divide to find the quotient: 3/5 ÷ 2/3

The calculator follows well-known rules for order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

Fractions in word problems:

  • Length subtracting
    meter_11 Express in mm: 5 3/10 cm - 2/5 mm
  • Add sub fractions
    fractions_2 What is 4 1/2+2/7-213/14?
  • Pizza fractions
    pizza Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • School
    skola_16 There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males?
  • Fractions mul add sum
    fractions_3 To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Difference mixed fractions
    mixed_fractions_1 What is the difference between 4 2/3 and 3 1/6?
  • Cake fractions
    dort Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
  • Pounds
    jablka_8 3 pounds subtract 1/3 of a pound.
  • Employees
    workers_45 Of all 360 employees, there are 11/12 women. How many men work in a company?
  • Package
    latky The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
  • Forty
    skola_2 Forty five of the 80 students were girls. What is the ratio of girls to boys?
  • Find the 24
    plusminus_1 Find the difference between 2/7 and 1/21
  • Coloured teacups
    venn The teacups in Tea Stop 55 are `2/5` green and `3/10` yellow. What fraction of the teacups are neither green nor yellow?


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